arXiv subjects

P. Khuntia

Publications and source records attributed to P. Khuntia.

At least 37 records · Page 2Linked to original sources

arXiv2024

Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11

Quantum magnets based on honeycomb lattices with low-coordination number offer a viable ground to realize exotic emergent quantum excitations and phenomena arising from the interplay between competing magnetic interactions, spin correlations, and spatial anisotropy. However, unlike their low-spin analogues, high-spin honeycomb lattice antiferromagnets have remained comparatively less explored in the context of capturing the classical analogs of quantum phenomena. Herein, we report the crystal structure, magnetic susceptibility, specific heat, and electron spin resonance (ESR), complemented by ab initio density functional theory (DFT) calculations on polycrystalline samples of FeP3SiO11 wherein the Fe3+ ions decorate a nearly-perfect S = 5/2 honeycomb lattice without any site disorder among constituent atoms. Above 150 K, an antiferromagnetic Weiss temperature of - 12 K is observed consistent with DFT calculations, which suggest the presence of strong intra-planar nearest-neighbor and weaker inter-planar further nearest-neighbor exchange interactions. An anomaly at TN = 3.5 K in specific heat and magnetic susceptibility reveals the presence of a long-range ordered ground state in zero field. Above TN, ESR evidences short-range spin correlations and unsaturated magnetic entropy, while below TN unconventional excitations are seen via power-law specific heat. A spin-flop transition is observed in an applied field of Hc1 = 0.2 T. At higher applied fields, TN is gradually suppressed down to zero at Hc2 = 5.6 T with a 2D critical exponent 0.255. Above Hc2, a broad maximum in specific heat due to gapped magnon excitations indicates the emergence of an interesting nearly-polarized state dressed by a disordered state in the honeycomb lattice antiferromagnet FeP3SiO11.

cond-mat.str-el↗

arXiv2024

Magnetism and spin dynamics of an S=3/2 frustrated trillium lattice antiferromagnet K2CrTi(PO4)3

Competing magnetic interactions, frustration driven quantum fluctuations, and spin correlations offer an ideal route for the experimental realization of emergent quantum phenomena and exotic quasi particle excitations in 3D frustrated magnets. In this context, trillium lattice, wherein magnetic ions decorate a three-dimensional chiral network of corner-shared equilateral triangular motifs, provides a viable ground. Herein, we present the crystal structure, magnetic susceptibility, specific heat, electron spin-resonance, muSR results on the polycrystalline samples of K2CrTi(PO4)3 wherein the Cr3+ ions form a perfect trillium lattice without any detectable anti-site disorder. The Curie-Weiss fit of the magnetic susceptibility data above 100 K yields a Curie-Weiss temperature of -23 K, which indicates the presence of dominant antiferromagnetic interactions between Cr3+ (S=3/2) moments. The specific heat measurements reveal the occurrence of two consecutive phase transitions, at temperatures TL = 4.3 K and TH = 8 K, corresponding to two different magnetic phases and it unveils the existence of short-range spin correlations above the ordering temperature TH. The power-law behavior of ESR linewidth suggests the persistence of short-range spin correlations over a relatively wide critical region in agreement with the specific heat results. The muSR resultsprovide concrete evidence of two different phases corresponding to two transitions, coupled with thecritical slowing down of spin fluctuations above TL and persistent spin dynamics below TL, consistent with the thermodynamic results. Moreover, the muSR results reveal the coexistence of static and dynamic local magnetic fields below TL, signifying the presence of complex magnetic phases owing to the entwining of spin correlations and competing magnetic interactions in this three-dimensional frustrated magnet.

cond-mat.str-el↗

arXiv2023

Experimental signatures of quantum and topological states in frustrated magnetism

Frustration in magnetic materials arising from competing exchange interactions can prevent the system from adopting long-range magnetic order and can instead lead to a diverse range of novel quantum and topological states with exotic quasiparticle excitations. Here, we review prominent examples of such emergent phenomena, including magnetically-disordered and extensively degenerate spin ices, which feature emergent magnetic monopole excitations, highly-entangled quantum spin liquids with fractional spinon excitations, topological order and emergent gauge fields, as well as complex particle-like topological spin textures known as skyrmions. We provide an overview of recent advances in the search for magnetically-disordered candidate materials on the three-dimensional pyrochlore lattice and two-dimensional triangular, kagome and honeycomb lattices, the latter with bond-dependent Kitaev interactions, and on lattices supporting topological magnetism. We highlight experimental signatures of these often elusive phenomena and single out the most suitable experimental techniques that can be used to detect them. Our review also aims at providing a comprehensive guide for designing and investigating novel frustrated magnetic materials, with the potential of addressing some important open questions in contemporary condensed matter physics.

cond-mat.str-el↗

arXiv2023

Magnetic properties and spin dynamics in a spin-orbit driven Jeff= 1/2 triangular lattice antiferromagnet

Frustration-induced strong quantum fluctuations accompanied by spin-orbit coupling and crystal electric field can give rise to rich and diverse magnetic phenomena associated with unconventional low-energy excitations in rare-earth based quantum magnets. Herein, we present crystal structure, magnetic susceptibility, specific heat, muon spin relaxation(muSR), and electron spin resonance (ESR) studies on the polycrystalline samples of Ba6Yb2Ti4O17 in which Yb3+ ions constitute a perfect triangular lattice in ab-plane without detectable anti-site disorder between atomic sites. The Curie-Weiss fit of low-temperature magnetic susceptibility data suggest the spin-orbit entangled Jeff = 1/2 degrees of freedom of Yb3+ spin with weak antiferromagnetic exchange interactions in the Kramers doublet ground state. The zero-field specific heat data reveal the presence of long-range magnetic order at TN = 77 mK which is suppressed in a magnetic field 1 T. The broad maximum in specific heat is attributed to the Schottky anomaly implying the Zeeman splitting of the Kramers doublet ground state. The ESR measurements suggest the presence of anisotropic exchange interaction between the moments of Yb3+ spins and the well separated Kramers doublet state. muSR experiments reveal a fluctuating state of Yb3+ spins in the temperature range 0.1 K-100 K owing to depopulation of crystal electric field levels, which suggests that the Kramers doublets are well separated consistent with thermodynamic and ESR results. In addition to the intraplane nearest-neighbor superexchange interaction, the interplane exchange interaction and anisotropy are expected to stabilize the long-range ordered state in this triangular lattice antiferromagnet.

cond-mat.str-el↗

arXiv2023

Magnetic properties of a spin-orbit entangled Jeff=1/2 three-dimensional frustrated rare-earth hyperkagome

The interplay between competing degrees of freedom can stabilize non-trivial magnetic states in correlated electron materials. Frustration-induced strong quantum fluctuations can evade long-range magnetic ordering leading to exotic quantum states such as spin liquids in two-dimensional spin-lattices such as triangular and kagome structures. However, the experimental realization of dynamic and correlated quantum states is rare in three-dimensional (3D) frustrated magnets wherein quantum fluctuations are less prominent. Herein, we report the crystal structure, magnetic susceptibility, electron spin resonance (ESR) and specific heat studies accompanied by crystal electric field (CEF) calculations on a 3D frustrated magnet Yb3Sc2Ga3O12. In this material, Yb3+ ions form a three-dimensional network of corner-sharing triangles known as hyperkagome lattice without any detectable anti-site disorder. Our results reveal a low energy state with Jeff = 1/2 degrees of freedom in the Kramers doublet state. The zero field-cooled and field cooled magnetic susceptibility taken in 0.001 T rules out the presence of spin-freezing down to 1.8K. The Curie-Weiss (CW) fit to low-T susceptibility data yields a small and negative CW temperature indicating the presence of a weak antiferromagnetic interaction between Jeff = 1/2 (Yb3+) moments. The Yb-ESR displays a broad line of non-Lorentzian shape that suggests considerable magnetic anisotropy in Yb3Sc2Ga3O12. The CEF calculations suggest that the ground state is well separated from the excited states, which are in good agreement with experimental results. The absence of long-range magnetic ordering indicates a dynamic liquid-like ground state at least down to 130 mK. Furthermore, zero field specific heat shows a broad maximum around 200 mK suggesting the presence of short-range spin correlations in this 3D frustrated antiferromagnet.

cond-mat.str-el↗

arXiv2023

Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice

The interplay between spin-orbit coupling, anisotropic magnetic interaction, frustration-induced quantum fluctuations and spin correlations can lead to novel quantum states with exotic excitations in rare-earth-based quantum magnets. Herein, we present the crystal structure, magnetization, electron spin resonance (ESR), specific heat, and nuclear magnetic resonance (NMR) experiments on the polycrystalline samples of Ba9Yb2Si6O24, in which Yb3+ ions form a perfect honeycomb lattice without detectable anti-site disorder. The magnetization data reveal antiferromagnetically coupled spin-orbit entangled Jeff = 1/2 degrees of freedom of Yb3+ ions in the Kramers doublet state. The ESR measurements reveal that the first excited Kramers doublet is 32.3(7) meV above the ground state. The specific heat results suggest the absence of any long-range magnetic order in the measured temperature range. Furthermore, the 29Si NMR results do not indicate any signature of magnetic ordering down to 1.6 K, and the spin-lattice relaxation rate reveals the presence of a field-induced gap that is attributed to the Zeeman splitting of Kramers doublet state in this quantum material. Our experiments detect neither spin freezing nor long-range magnetic ordering down to 1.6 K. The current results suggest the presence of short-range spin correlations in this spin-orbit entangled Jeff =1/2 rare-earth magnet on a honeycomb lattice.

cond-mat.str-el↗

arXiv2022

Electronic structure and magnetic properties of 3d-4f double perovskite material

Double perovskite-based magnets wherein frustration and competition between emergent degrees of freedom are at play can lead to novel electronic and magnetic phenomena. Herein, we report the electronic structure and magnetic properties of an ordered double perovskite material Ho2CoMnO6. In the double perovskite with general class A2BB'O6, the octahedral B and B'-site has a distinct crystallographic site. The Rietveld refinement of XRD data reveals that Ho2CoMnO6 crystallizes in the monoclinic P21/n space group. The X-ray photoelectron spectroscopy confirms the charge state of cations present in this material. The temperature dependence of magnetization and specific heat exhibit a long-range ferromagnetic ordering at Tc ~ 76 K owing to the presence of super exchange interaction between Co2+ and Mn4+ moments. Furthermore, the magnetization isotherm at 5 K shows a hysteresis curve that confirms ferromagnetic behavior of this double perovskite. We observed a re-entrant glassy state in the intermediate temperature regime, which is attributed to inherent anti-site disorder and competing interactions. A large magnetocaloric effect has been observed much below the ferromagnetic transition temperature. The temperature-dependent Raman spectroscopy studies support the presence of spin-phonon coupling and short-range order above Tc in this double perovskite. The stabilization of magnetic ordering and charge states is further analyzed through electronic structure calculations. The latter also infers the compound to be a narrow band gap insulator with the gap arising between the lower and upper Hubbard Co-d subbands. Our results demonstrate that anti-site disorder and complex 3d-4f exchange interactions in the spin-lattice account for the observed electronic and magnetic properties in this promising double perovskite material.

cond-mat.mtrl-sci↗

arXiv2022

The $S=1$ dimer system K$_2$Ni(MoO$_4$)$_2$: a candidate for magnon Bose-Einstein condensation

Dimerized quantum magnets provide a unique possibility to investigate Bose-Einstein condensation of magnetic excitations in crystalline systems at low temperature. Here, we model the low-temperature magnetic properties of the recently synthesized spin $S=1$ dimer system K${}_2$Ni(MoO${}_4$)$_2$ and propose it as a new candidate material for triplon and quintuplon condensation. Based on a first principles analysis of its electronic structure, we derive an effective spin-dimer model that we first solve within a mean-field approximation to refine its parameters in comparison to experiment. Finally, the model is solved by employing a numerically exact quantum Monte Carlo technique which leads to magnetic properties in good agreement with experimental magnetization and thermodynamic results. We discuss the emergent spin model of K${}_2$Ni(MoO${}_4$)$_2$ in view of condensation of magnetic excitations in a broad parameter regime. Finally, we comment on a geometrical peculiarity of the proposed model and discuss how it could host a supersolid phase upon structural distortions.

cond-mat.str-el↗

arXiv2022

Spin liquid state in a rare-earth hyperkagome lattice

Quantum fluctuations enhanced by frustration and subtle interplay between competing degrees of freedom offer an ideal ground to realize novel states with fractional quantum numbers in quantum materials that defy standard theoretical paradigms. Quantum spin liquid (QSL) is a highly entangled state wherein frustration induced strong quantum fluctuations preclude symmetry breaking phase transitions down to zero temperature without any order parameter. Experimental realizations of QSL in quantum materials with spin dimensionality greater than one is very rare. Here, we present our thermodynamic, nuclear magnetic resonance, muon spin relaxation and inelastic neutron scattering studies of a new rare-earth hyperkagome compound Li3Yb3Te2O12 in which Yb3+ ions constitute a three dimensional spin-lattice without any detectable disorder. Our comprehensive experiments evince neither signature of magnetic ordering nor spin freezing down to 38 mK that suggest the realization of dynamic liquid-like ground state in this antiferromagnet. The ground state of this material is interpreted by a low energy Jeff = 1/2 degrees of freedom with short range spin correlations. The present results demonstrate a viable basis to explore spin-orbit driven enigmatic correlated quantum states in a new class of rare-earth based three dimensional frustrated magnets that may open new avenues in theoretical and experimental search for spin liquids.

cond-mat.str-el↗

arXiv2022

Magnetic properties of triangular lattice antiferromagnets Ba3RB9O18 (R = Yb, Er)

Frustration, spin correlations and interplay between competing degrees of freedom are some of the key ingredients that underlie exotic states with fractional excitations in quantum materials. Rare-earth based two dimensional magnetic lattice wherein crystal electric field, spin-orbit coupling, anisotropy and electron correlation between rare-earth moments offer a new paradigm in this context. Herein, we present crystal structure, magnetic susceptibility and specific heat accompanied by crystal electric field calculations on the polycrystalline sample of Ba3RB9O18 (R = Yb, Er) in which R3+ ions form a perfect triangular lattice without anti-site disorder. The localized R3+ spins show neither long-range order nor spin-glass state down to 1.9 K in Ba3RB9O18. Magnetization data reveal a pseudospin Jeff = 1/2 ( Yb3+) in the Kramers doublet state and a weak antiferromagnetic interaction between Jeff = 1/2 moments in the Yb variant. On the other hand, the effective moment μeff = 8.8 μB was obtained from the Curie-Weiss fit of the low-temperature susceptibility data of Er variant suggests the admixture of higher crystal electric field states with the ground state. The Curie-Weiss fit of low-temperature susceptibility data for Er system unveils the presence of a relatively strong antiferromagnetic interaction between Er3+ moments compared to its Yb3+ analog. Ba3ErB9O18 does not show long-range magnetic ordering down to 500 mK. Furthermore, our crystal electric field calculations based on magnetization data of Ba3ErB9O18 suggest the presence of a small gap between the ground and first excited Kramers doublets. The broad maximum around 4 K in magnetic specific heat in zero-field is attributed to the thermal population of the first CEF excited state in Ba3ErB9O18, which is consistent with our CEF calculations.

cond-mat.str-el↗

arXiv2022

Signature of a randomness-driven spin-liquid state in a frustrated magnet

Collective behaviour of electrons, frustration induced quantum fluctuations and entanglement in quantum materials underlie some of the emergent quantum phenomena with exotic quasi-particle excitations that are highly relevant for technological applications. Herein, we present our thermodynamic and muon spin relaxation measurements, complemented by ab initio density functional theory and exact diagonalization results, on the recently synthesized frustrated antiferromagnet Li4CuTeO6, in which Cu2+ ions (S = 1/2) constitute disordered spin chains and ladders along the crystallographic [101] direction with weak random inter-chain couplings. Our thermodynamic experiments detect neither long-range magnetic ordering nor spin freezing down to 45 mK despite the presence of strong antiferromagnetic interaction between Cu2+ moments leading to a large effective Curie-Weiss temperature of -154 K. Muon spin relaxation results are consistent with thermodynamic results. The temperature and magnetic field scaling of magnetization and specific heat reveal a data collapse pointing towards the presence of random-singlets within a disorder-driven correlated and dynamic ground-state in this frustrated antiferromagnet.

cond-mat.str-el↗

arXiv2022

Quantum spin liquid in the Ising triangular-lattice antiferromagnet neodymium heptatantalate

Disordered magnetic states known as spin liquids are of paramount importance in both fundamental and applied science. A classical state of this kind was predicted for the Ising antiferromagnetic triangular model more than half a century ago, while additional non-commuting exchange terms were proposed to induce its quantum version -- a quantum spin liquid. These predictions have not been yet confirmed experimentally. Here we report a discovery of such a state in the structurally perfect triangular-lattice antiferromagnet NdTa$_7$O$_{19}$. Its magnetic ground state is characterized by spin-1/2 degrees of freedom with Ising-like interactions and gives rise to low-frequency spin excitations persisting down to the lowest temperatures. Our study demonstrates the key role of strong spin-orbit coupling in stabilizing spin liquids that result from magnetic anisotropy and highlights the large family of rare-earth (RE) heptatantalates RETa$_7$O$_{19}$ as a novel framework for realization of these states, which represent a promising platform for quantum applications.

cond-mat.str-el↗

arXiv2021

Magnetic properties of S = 5/2 anisotropic triangular chain Bi3FeMo2O12

Competing magnetic interactions in low-dimensional quantum magnets can lead to the exotic ground state with fractionalized excitations. Herein, we present our results on an S = 5/2 quasi-one-dimensional spin system Bi3FeMo2O12. The structure of Bi3FeMo2O12 consists of very well separated, infinite zig-zag S = 5/2 spin chains. The observation of a broad maximum around 10 K in the magnetic susceptibility suggests the presence of short-range spin correlations. Magnetic susceptibility data do not fit to S=5/2 uniform spin chain model due to the presence of 2nd nearest-neighbor coupling (J2) along with the 1st nearest-neighbor coupling J1 of the zig-zag chain. The electronic structure calculations infer that the value of J1 is comparable with J2 (J2/J1~1.1) with a negligible inter-chain interaction (J'/J ~ 0.01), implying that Bi3FeMo2O12 is a highly frustrated triangular chain system. The absence of magnetic long-range ordering down to 0.2 K is seen in the heat capacity data, despite a relatively large antiferromagnetic Curie-Weiss temperature of -40 K. The magnetic heat capacity follows nearly a linear behavior at low temperatures indicating that the S = 5/2 anisotropic triangular chain exhibits the gapless excitations.

cond-mat.str-el↗

arXiv2020

Development of short and long-range magnetic order in the double perovskite based frustrated triangular lattice antiferromagnet Ba2MnTeO6

Oxide double perovskites wherein octahedra formed by both 3d elements and sp-based heavy elements give rise to unconventional magnetic ordering and correlated quantum phenomena crucial for futuristic applications. Here, by carrying out experimental and first principles investigations, we present the electronic structure and magnetic phases of Ba2MnTeO6, where Mn^2+ ions with S = 5/2 spins constitute a perfect triangular lattice. The magnetic susceptibility reveals a large Curie- Weiss temperature -152 K suggesting the presence of strong antiferromagnetic interactions between Mn^2+ moments in the spin lattice. A phase transition at 20 K is revealed by magnetic susceptibility and specific heat which is attributed to the presence of a sizeable inter-plane interactions. Below the transition temperature, the specific heat data show antiferromagnetic magnon excitations with a gap of 1.4 K. Furthermore, muon spin-relaxation reveals the presence of static internal fields in the ordered state and provides strong evidence of short-range spin correlations for T > TN. The DFT+U calculations and spin-dimer analysis infer that Heisenberg interactions govern the inter and intra-layer spin-frustrations in this perovskite. The inter and intra-layer exchange interactions are of comparable strengths (J1 = 4.6 K, J2 = 0.92 J1). However, a weak third nearest-neighbor ferromagnetic inter-layer interaction exists (J3=-0.04 J1) due to double-exchange interaction via the linear path Mn-O-Te-O-Mn. The combined effect of J2 and J3 interactions stabilizes a three dimensional long-range magnetic ordering in this frustrated magnet.

cond-mat.str-el↗

arXiv2019

Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu$_3$(OH)$_6$Cl$_2$

Spin liquids are exotic phases of quantum matter challenging Landau's paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. While well-established for 1D quantum antiferromagnets, in higher dimension where quantum fluctuations are less acute, realizing and understanding such states represent major issues, both theoretical and experimental. In this respect the simplest nearest-neighbor Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key-issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature Nuclear Magnetic Resonance (NMR) contrast experiments on high quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$. We firmly conclude that this material does not harbor any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet.

cond-mat.str-el↗

arXiv2017

Persistent low-temperature spin dynamics in the mixed-valence iridate Ba$_{3}$InIr$_{2}$O$_{9}$

Using thermodynamic measurements, neutron diffraction, nuclear magnetic resonance, and muon spin relaxation, we establish putative quantum spin-liquid behavior in Ba$_3$InIr$_2$O$_9$, where unpaired electrons are localized on mixed-valence Ir$_2$O$_9$ dimers with Ir$^{4.5+}$ ions. Despite the antiferromagnetic Curie-Weiss temperature on the order of 10 K, neither long-range magnetic order nor spin freezing are observed down to at least 20 mK, such that spins are short-range correlated and dynamic over nearly three decades in temperature. Quadratic power-law behavior of both the spin-lattice relaxation rate and specific heat indicates the gapless nature of the ground state. We envisage that this exotic behavior may be related to an unprecedented combination of the triangular and buckled honeycomb geometries of nearest-neighbor exchange couplings in the mixed-valence setting.

cond-mat.str-el↗

arXiv2017

Local Magnetism and Spin Dynamics of the Frustrated Honeycomb Rhodate Li2RhO3

We report magnetization, heat capacity, 7Li - nuclear magnetic resonance (NMR), and muSR (muon spin roration) measurements on the honeycomb 4d5 spin liquid candidate Li2RhO3. The magnetization in small magnetic fields provides evidence of the partial spin-freezing of a small fraction of Rh4+ -moments at 6 K, whereas the Curie-Weiss behavior above 100 K suggests a pseudo-spin-1/2 paramagnet with a moment of about 2.2 muB. The magnetic specific heat (Cm) exhibits no field dependence and demonstrates the absence of long range magnetic order down to 0.35 K. Cm/T passes through a broad maximum at about 10 K and Cm=T^2 at low temperatures. Measurements of the spin-lattice relaxation rate (1/T1) reveal a gapless slowing down of spin fluctuations upon cooling with 1/T1=T^2.2. The results from NMR and muSR are consistent with a scenario in which a minority of Rh4+ moments are in a ahort-range correlated frozen state and coexist with a majority of moments in a liquid-like state that continue to fluctuate at low temperatures.

cond-mat.str-el↗

arXiv2017

Bose-Einstein condensation of triplons in the S=1 tetramer antiferromagnet K2Ni2(MoO4)3: A compound close to quantum critical point

The structure of K2Ni2(MoO4)3 consists of S=1 tetramers formed by Ni^{2+} ions. The magnetic susceptibility chi(T) and specific heat Cp(T) data on a single crystal show a broad maximum due to the low-dimensionality of the system with short-range spin correlations. A sharp peak is seen in chi(T) and Cp(T) at about 1.13 K, well below the broad maximum. This is an indication of magnetic long-range order i.e., the absence of spin-gap in the ground state. Interestingly, the application of a small magnetic field (H>0.1 T) induces magnetic behavior akin to Bose-Einstein condensation (BEC) of triplon excitations observed in some spin-gap materials. Our results demonstrate that the temperature-field (T-H) phase boundary follows a power-law (T-T_{N})propotional to H^(1/alpha) with the exponent 1/alpha close to 2/3, as predicted for BEC scenario. The observation of BEC of triplon excitations in small H infers that K2Ni2(MoO4)3 is located in the proximity of a quantum critical point, which separates the magnetically ordered and spin-gap regions of the phase diagram.

cond-mat.str-el↗